Puzzles with numbers and things

[davis_greatest]

Hehe. Go on, robert, you can explain. I'm struggling a bit for time today. Maybe then we can share the point.

[snookersfun]

Just in case DGE gets his explanation so horribly wrong that he can't possibly be awarded the point, I'll chip in with 22cm .

another good answer here! So, who wants to give the explanation?

[Robert602]

I'm going to assume I can say that that triangle is right angled (at C) without proving it, as it's just high school geometry.

We know that:
a^2 + b^2 = 100 (pythagoras)
0.5ab = 11 (area of the triangle) -> 2ab=44

Add them together:
a^2 + b^2 + 2ab = 144

Then factorise
(a+b)^2 = 144
a+b = 12

and so the perimeter is 12+10 = 22

[snookersfun]

Robert rejoined the race!

Well done, Robert. I think your proof is even rather elegant! So. you deserve the point.
I also let you use the right angle and Pythagoras (although DG might have had to prove those parts as well )

I'm going to assume I can say that that triangle is right angled (at C) without proving it, as it's just high school geometry.

We know that:
a^2 + b^2 = 100 (pythagoras)
0.5ab = 11 (area of the triangle) -> 2ab=44

Add them together:
a^2 + b^2 + 2ab = 144

Then factorise
(a+b)^2 = 144
a+b = 12

and so the perimeter is 12+10 = 22

[snookersfun]

One point for Robert (which catapults him into 3rd place) and one for davis-greatest (in accord with the special rule; we will allow him until he'll get dangerous)

HERE IS THE SCOREBOARD AFTER ROUND 30

snookersfun……………………….…..14
Vidas……………………………………….8½
robert602…………………………………5
abextra……………………………..…...4½
davis_greatest…………………..……3

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

hope that is OK, DG?

__________________

[davis_greatest]

Looks good!

[Robert602]

Very generous of you SF, and DGE. I reckon I nicked a point there but I'm not going to complain.

It's a bit hectic here at the moment but I'll post a few questions of my own as soon as I get the chance.

[snookersfun]

DG, Norman and Charlie awfully busy???

[davis_greatest]

Question 31 - Reciprocate this!

DG, Norman and Charlie awfully busy???

Who's Norman?

Charlie has been a bit busy, teaching Oliver, Gordon and me about numbers that aren't whole numbers (did you know that there exist "non-integers"?) and about reciprocals. Apparently, the reciprocal of a number is "one divided by that number". So, the reciprocal of 2 is 1/2 = one half, and the reciprocal of 10 is 0.1. Oliver and Gordon are now experts, and I'm beginning to understand them too.

Now that we know about non-integers, we can do calculations with them.

So, to test us, Charlie comes up with a special number, which he calls Special Number. He tells me the Special Number, and he tells Gordon the square of the Special Number, and tells Oliver the cube of the Special Number.

Then, I have to add my number to its reciprocal. I get a whole number, with more than one digit.

Gordon has to add his number to its reciprocal. He also gets a whole number, with the same number of digits as my answer.

Oliver also has to add his number to its reciprocal. Without using a calculator or computer, what answer did Oliver get?

[abextra]

I only wish Charlie would tell me the fourth power of the Special Number...

[snookersfun]

970, 980ish?
I feel a bit silly, the question sounded so easy initially...

[davis_greatest]

970, 980ish?
I feel a bit silly, the question sounded so easy initially...

Charlie says yes-ish, but to give the point he wants a single exact answer.

[elvaago]

What the heck is the cube of a number?

[snookersfun]

hopefully 970, after a bit more thought.

Elvago
square-two dimensional nxn or n^2 (gives the area of a square)
cube-three dimensional nxnxn or n^3 (gives the volume of a cube)

[elvaago]

Thank you.